Browsing by Author "Hoffman, Dean"

Now showing items 21-34 of 34

A New Solution to the Intersection Problem of Mendelsohn Triple Systems

Watson, Rachel (2012-03-29)

The thesis provides an alternate solution to the intersection problem, in which the goal is to determine the set of all values for which there exists a pair of Mendelsohn Triple Systems having this exact value of cyclic ...

Nim on Graphs

Clark, Jonathan (2012-08-02)

Winning strategies for the Game of Nim on Graphs are discussed. Graphs considered are distinguished from those previously studied in that they may have loops. Winning strategies are found for graphs that have loops and ...

On Frobenius numbers in three variables

Trimm, Janet (2006-08-15)

Given a set of relatively prime positive integers $\{a_1,a_2,\ldots, a_n\}$, after some point all positive integers are representable as a linear combination of the set with nonnegative coefficients. Which integer is the ...

On the Independence Number of Some Hypergraph

Yang, Zechun (2018-07-10)

For integers 1 =< m < n and a prime p (we require 2 =< m when p = 2), a subset I(p^n; p^m) ={0,...,p^n-1} is described which contains no pm-term cyclic arithmetic progression modulo p^n, and which is maximal among subsets ...

On the Spectrum of Minimal Covers By Triples

Castellana, Vincent (2006-08-15)

A Minimal Cover by Triples is an ordered pair (V,T) where V is a finite set and T is a collection of three element subsets of V with two properties. First, that every pair of elements of V appear together in at least ...

Path and Cycle Decompositions

Dinavahi, Venkatasai (2008-08-15)

A $G$-design is a partition of edge set of K_v in which each element induces a copy of G. The existence of G-designs with the additional property that they contain no proper subsystems has been previously settled when G ...

Path Decompositions of the Kneser Graph

Whitt, Thomas Richard, III (2013-04-22)

Necessary and sufficient conditions are given for the existence of a graph decomposition of the Kneser Graph $KG_{n,2}$ into paths of length three and four, and of the Generalized Kneser Graph $GKG_{n,3,1}$ into paths of ...

Revisiting the Intersection Problem for Maximum Packings of K_(6n+5) with Triples

Holmes, Amber (2017-04-16)

In 1989, Gaetano Quattrocchi gave a complete solution of the intersection problem for maximum packings of K_(6n+5) with triples when the leave (a 4--cycle) is the same in each maximum packing. Quattrocchi showed that I[2]=2 ...

Security, (F,I)-security, and Ultra-security in Graphs

Petrie, Caleb (2012-08-02)

Let G=(V,E) be a graph and S a subset of V. The notion of security in graphs was first presented by Brigham et al [3]. A set S is secure if every attack on S is defendable. The cardinality of a smallest secure set of G ...

The Shields-Harary Number of Graphs

Holliday, John (2004-05-15)

The Shields-Harary numbers are a class of graph paramaters that measure the robustness of a graph in terms of network vulnerability, with reference to a given cost function.

Some Necessary Conditions for List Colorability of Graphs and a Conjecture on Completing Partial Latin Squares

Bobga, Benkam (2008-12-15)

Let C be an infinite set of symbols, F the collection of finite subsets of C. A function L is a list assignment to a graph G if L assigns to each vertex of G a finite subset of C. A proper L-coloring occurs when adjacent ...

Stars and Hyperstars

Roberts, Dan (2012-07-02)

A \textit{$k$-star} is a complete bipartite graph $K_{1,k}$, and a hypergraph $G=(X,\mathcal{E})$ is a \textit{hyperstar} with center $C$ if $\displaystyle C\subseteq\bigcap_{E\in\mathcal{E}}E$. Given (hyper)graphs $G$ ...

Structure Theory and a Generalization of the Isomorphism Theorems

Bertl, Alan (2013-07-10)

A general format in which the mathematical structure of topological spaces, algebraic structures, and graphs can be expressed is described. A generalization of the fundamental homomorphism theorem and the isomorphism ...

The Triangle Intersection Problem For Hexagon Triple Systems

Pettis, Carl (2006-08-15)

The Triangle Intersection Problem for Hexagon Triple Systems Carl S. Pettis, Auburn University A hexagon triple is the graph and a hexagon triple system is an edge disjoint decomposition of ...